Statistics Homework Solutions 166

# Statistics Homework Solutions 166 - 166 CHAPTER 6 0 versus...

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Unformatted text preview: 166 CHAPTER 6 0 versus H1 : median of X median of Y ยก median of Y ยก ยก The test statistic W is the sum of the ranks corresponding to the X sample. 281 5. The sample sizes are m 15 and n 15. ยก ยก ยจ W ยก Since n and m are both greater than 8, compute the z-score of W and use the z table. mm n 1 2 mn m n 1 12 2 03. ยฃ ยฅ ยก ยข ยฃ ยฅ ยข ยค ยข ยก ยข W ยจ โ, the P-value is the sum of the areas ยก ยจ 0 0424. ยจ ยก 0 0212 ยก ยจ ยข 0 0212 ยจ ยจ ยก From the z table, P median of Y ยก Since the alternate hypothesis is of the form median of X to the right of z 2 03 and to the left of z 2 03. ยก ยก ยค z ยก The P-value is fairly small, and so it provides reasonably strong evidence that the population medians are different. (c) No, the X sample is heavily skewed to the right, while the Y sample is strongly bimodal. It does not seem reasonable to assume that these samples came from populations of the same shape. 19. (a) Let ยตA be the mean thrust/weight ratio for Fuel A, and let ยตB be the mean thrust/weight ratio for Fuel B. The appropriate null and alternate hypotheses are H0 : ยตA ยตB 0 versus H1 : ยตA ยตB 0. ยก ยก ยก ยจ 53 019, sB ยจ ยก 16, B 2 7294, nB ยก ยก 2 5522, nA ยจ ยจ ยก 54 919, sA 16. ยก ยจ ยก (b) A The number of degrees of freedom is 2 2 72942 16 2 72942 16 16 1 ยข 2 ยฅ ยฃ ยจ ยค 29, rounded down to the nearest integer. ยข ยก ยตB 0. โ, the P-value is the area to the right of t ยก ยก ยฉยฃยฅ 0 05. A computer package gives P 2 0339. 0 026. ยจ ยก ยจ ยจ ยก ยก ยจ ยค ยก ยจ ยก ยก ยจ 0 05, we can conclude at the 5% level that the means are different. ยจ ยจ Since P P ยตB 0 versus H1 : ยตA ยก ยฃ From the t table, 0 025 ยจ ยข ยก ยก ยค Since the alternate hypothesis is of the form ยตA ยตB ยจ ยจ ยจ The null and alternate hypotheses are H0 : ยตA 2 0339. ยก 2 72942 16 ยฃ 2 55222 16 ยก 0 ยจ ยฃ ยก 53 019 ยก ยฅ 54 919 ยก ยจ t29 ยจ ฮฝ ยก 2 55222 16 2 55222 16 2 16 1 21. (a) Yes. (b) The conclusion is not justi๏ฌed. The engineer is concluding that H0 is true because the test failed to reject. 65, O 2 ยก ยก ยก ยก ยฃ j O , as shown in the following table. Oi O ยก The expected values are Ei j 216. The column totals are O 1 ยก 214 and O2 121, O 3 The row totals are O1 total is O 430. ยก 23. 244. The grand ยก The null and alternate hypotheses are H0 : median of X 0. ...
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